Answer:
Number that belongs in the green box (rounded to the nearest hundredth) = 16.62
Explanation:
Finding the angle using the Law of Sines:
- Because we don't know whether this is a right triangle, we can use the Law of Sines to find the measure of the angle (let's call it A).
- This Law can be used to calculate an unknown angle in a non-right triangle when two sides and one angle opposite on of the sides is known.
The Law of Sines works through proportions between the sines of a triangle's angles and the sides opposite these angles:
a / sin A = b / sin B = c / sin C
Thus, we can substitute 6.78 for b, the 29° angle for B, and 4 for a in the Law of Sines to find A, the measure of the unknown angle to the nearest hundredth:
(4 / sin A = 6.78 / sin 29) * sin A
(4 = (6.78 / sin 29) * sin A) / 6.78 / sin 29
4 / (6.78 / sin 29) = sin A
sin^-1 (4 / (6.78 / sin 29)) = A
16.62003032 = A
16.62 = A
Thus, the measure of the unknown angle is about 16.62°.